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<a href="classEigen_1_1LDLT-members.html">List of all members</a> &#124;
<a href="#pub-methods">Public Member Functions</a>  </div>
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<div class="title">Eigen::LDLT&lt; MatrixType_, UpLo_ &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__DenseLinearSolvers__chapter.html">Dense linear problems and decompositions</a> &raquo; <a class="el" href="group__DenseLinearSolvers__Reference.html">Reference</a> &raquo; <a class="el" href="group__Cholesky__Module.html">Cholesky module</a></div></div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename MatrixType_, int UpLo_&gt;<br />
class Eigen::LDLT&lt; MatrixType_, UpLo_ &gt;</h3>

<p>Robust Cholesky decomposition of a matrix with pivoting. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
  <table class="tparams">
    <tr><td class="paramname">MatrixType_</td><td>the type of the matrix of which to compute the LDL^T Cholesky decomposition </td></tr>
    <tr><td class="paramname">UpLo_</td><td>the triangular part that will be used for the decomposition: Lower (default) or Upper. The other triangular part won't be read.</td></tr>
  </table>
  </dd>
</dl>
<p>Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite matrix \( A \) such that \( A = P^TLDL^*P \), where P is a permutation matrix, L is lower triangular with a unit diagonal and D is a diagonal matrix.</p>
<p>The decomposition uses pivoting to ensure stability, so that D will have zeros in the bottom right rank(A) - n submatrix. Avoiding the square root on D also stabilizes the computation.</p>
<p>Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky decomposition to determine whether a system of equations has a solution.</p>
<p>This class supports the <a class="el" href="group__InplaceDecomposition.html">inplace decomposition </a> mechanism.</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a0ecf058a0727a4cab8b42d79e95072e1">MatrixBase::ldlt()</a>, <a class="el" href="classEigen_1_1SelfAdjointView.html#a644155eef17b37c95d85b9f65bb49ac4">SelfAdjointView::ldlt()</a>, class <a class="el" href="classEigen_1_1LLT.html" title="Standard Cholesky decomposition (LL^T) of a matrix and associated features.">LLT</a> </dd></dl>
</div><div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
  <img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for Eigen::LDLT&lt; MatrixType_, UpLo_ &gt;:</div>
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Public Member Functions</h2></td></tr>
<tr class="memitem:af4fd7733fd47bc76d49d8dde08494195"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1LDLT.html">LDLT</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#af4fd7733fd47bc76d49d8dde08494195">adjoint</a> () const</td></tr>
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<tr class="memitem:a18589fe69cc1286c3da6ad894813899c"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:a18589fe69cc1286c3da6ad894813899c"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1LDLT.html">LDLT</a>&lt; MatrixType, UpLo_ &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#a18589fe69cc1286c3da6ad894813899c">compute</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;a)</td></tr>
<tr class="separator:a18589fe69cc1286c3da6ad894813899c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae24d5a022e1c09d5afa0e84c356b854e"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#ae24d5a022e1c09d5afa0e84c356b854e">info</a> () const</td></tr>
<tr class="memdesc:ae24d5a022e1c09d5afa0e84c356b854e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Reports whether previous computation was successful.  <a href="classEigen_1_1LDLT.html#ae24d5a022e1c09d5afa0e84c356b854e">More...</a><br /></td></tr>
<tr class="separator:ae24d5a022e1c09d5afa0e84c356b854e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a87fc4b3b96a1f432374541defad416f9"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#a87fc4b3b96a1f432374541defad416f9">isNegative</a> (void) const</td></tr>
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<tr class="memitem:aa1294edd3e62b4b1906918abc75ae50e"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#aa1294edd3e62b4b1906918abc75ae50e">isPositive</a> () const</td></tr>
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<tr class="memitem:a9ab5fbbe154dd5b43fe272126d69411f"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#a9ab5fbbe154dd5b43fe272126d69411f">LDLT</a> ()</td></tr>
<tr class="memdesc:a9ab5fbbe154dd5b43fe272126d69411f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor.  <a href="classEigen_1_1LDLT.html#a9ab5fbbe154dd5b43fe272126d69411f">More...</a><br /></td></tr>
<tr class="separator:a9ab5fbbe154dd5b43fe272126d69411f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab45453a84ebb985cb0d1d9128b7af18d"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:ab45453a84ebb985cb0d1d9128b7af18d"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#ab45453a84ebb985cb0d1d9128b7af18d">LDLT</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="memdesc:ab45453a84ebb985cb0d1d9128b7af18d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor with decomposition.  <a href="classEigen_1_1LDLT.html#ab45453a84ebb985cb0d1d9128b7af18d">More...</a><br /></td></tr>
<tr class="separator:ab45453a84ebb985cb0d1d9128b7af18d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad2f39b7a2a17c6e982db2e4164b6dd9f"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:ad2f39b7a2a17c6e982db2e4164b6dd9f"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#ad2f39b7a2a17c6e982db2e4164b6dd9f">LDLT</a> (<a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="memdesc:ad2f39b7a2a17c6e982db2e4164b6dd9f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructs a <a class="el" href="classEigen_1_1LDLT.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> factorization from a given matrix.  <a href="classEigen_1_1LDLT.html#ad2f39b7a2a17c6e982db2e4164b6dd9f">More...</a><br /></td></tr>
<tr class="separator:ad2f39b7a2a17c6e982db2e4164b6dd9f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abd3c8856337dfc7f4df6214b9503dcf2"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#abd3c8856337dfc7f4df6214b9503dcf2">LDLT</a> (<a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="el" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a>)</td></tr>
<tr class="memdesc:abd3c8856337dfc7f4df6214b9503dcf2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor with memory preallocation.  <a href="classEigen_1_1LDLT.html#abd3c8856337dfc7f4df6214b9503dcf2">More...</a><br /></td></tr>
<tr class="separator:abd3c8856337dfc7f4df6214b9503dcf2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1c29cf5110c180a8fc5da40096822ed1"><td class="memItemLeft" align="right" valign="top">Traits::MatrixL&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#a1c29cf5110c180a8fc5da40096822ed1">matrixL</a> () const</td></tr>
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<tr class="memitem:a3b8250ff102497021676df9f8cb76113"><td class="memItemLeft" align="right" valign="top">const MatrixType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#a3b8250ff102497021676df9f8cb76113">matrixLDLT</a> () const</td></tr>
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<tr class="memitem:ae8be83b613c7fad1ad5d0a2b44c483e0"><td class="memItemLeft" align="right" valign="top">Traits::MatrixU&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#ae8be83b613c7fad1ad5d0a2b44c483e0">matrixU</a> () const</td></tr>
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<tr class="memitem:a21a4d19e6c079967ee96c808a8e91d68"><td class="memTemplParams" colspan="2">template&lt;typename Derived &gt; </td></tr>
<tr class="memitem:a21a4d19e6c079967ee96c808a8e91d68"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1LDLT.html">LDLT</a>&lt; MatrixType, UpLo_ &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#a21a4d19e6c079967ee96c808a8e91d68">rankUpdate</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Derived &gt; &amp;w, const typename <a class="el" href="classEigen_1_1LDLT.html">LDLT</a>&lt; MatrixType, UpLo_ &gt;::RealScalar &amp;sigma)</td></tr>
<tr class="separator:a21a4d19e6c079967ee96c808a8e91d68"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a69bc9dfd866eab90646ca7b74e52c8bc"><td class="memItemLeft" align="right" valign="top">RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#a69bc9dfd866eab90646ca7b74e52c8bc">rcond</a> () const</td></tr>
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<tr class="memitem:adf2c9a2939f6c5f4e36a94d99d4aa49f"><td class="memItemLeft" align="right" valign="top">MatrixType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#adf2c9a2939f6c5f4e36a94d99d4aa49f">reconstructedMatrix</a> () const</td></tr>
<tr class="separator:adf2c9a2939f6c5f4e36a94d99d4aa49f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3ed6b348086c7b4c117dbff35be1a16d"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#a3ed6b348086c7b4c117dbff35be1a16d">setZero</a> ()</td></tr>
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<tr class="memitem:a20cfad0f8808c84d150d1f90abe1fc87"><td class="memTemplParams" colspan="2">template&lt;typename Rhs &gt; </td></tr>
<tr class="memitem:a20cfad0f8808c84d150d1f90abe1fc87"><td class="memTemplItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1LDLT.html">LDLT</a>, Rhs &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#a20cfad0f8808c84d150d1f90abe1fc87">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
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<tr class="memitem:a0779d1ee8b62a8a97275dc36db340a35"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Transpositions.html">TranspositionType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#a0779d1ee8b62a8a97275dc36db340a35">transpositionsP</a> () const</td></tr>
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<tr class="memitem:a1d536082297052c96f074c5e208bb7a8"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Diagonal.html">Diagonal</a>&lt; const MatrixType &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LDLT.html#a1d536082297052c96f074c5e208bb7a8">vectorD</a> () const</td></tr>
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<tr class="inherit_header pub_methods_classEigen_1_1SolverBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_classEigen_1_1SolverBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="classEigen_1_1SolverBase.html">Eigen::SolverBase&lt; LDLT&lt; MatrixType_, UpLo_ &gt; &gt;</a></td></tr>
<tr class="memitem:ae1025416bdb5a768f7213c67feb4dc33 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const AdjointReturnType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#ae1025416bdb5a768f7213c67feb4dc33">adjoint</a> () const</td></tr>
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<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1LDLT.html">LDLT</a>&lt; MatrixType_, UpLo_ &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
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<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1LDLT.html">LDLT</a>&lt; MatrixType_, UpLo_ &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
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<tr class="memitem:a7fd647d110487799205df6f99547879d inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1LDLT.html">LDLT</a>&lt; MatrixType_, UpLo_ &gt;, Rhs &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a7fd647d110487799205df6f99547879d">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
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<tr class="memitem:a4d5e5baddfba3790ab1a5f247dcc4dc1 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a4d5e5baddfba3790ab1a5f247dcc4dc1">SolverBase</a> ()</td></tr>
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<tr class="memitem:a70cf5cd1b31dbb4f4d61c436c83df6d3 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Transpose.html">ConstTransposeReturnType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a70cf5cd1b31dbb4f4d61c436c83df6d3">transpose</a> () const</td></tr>
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<tr class="inherit_header pub_methods_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a2d768a9877f5f69f49432d447b552bfe inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">cols</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
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<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">const Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
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<tr class="memitem:ac22eb0695d00edd7d4a3b2d0a98b81c2 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:ae106171b6fefd3f7af108a8283de36c9 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="inherited"></a>
Additional Inherited Members</h2></td></tr>
<tr class="inherit_header pub_types_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_types_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Types inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a></td></tr>
<tr class="memdesc:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="mdescLeft">&#160;</td><td class="mdescRight">The interface type of indices.  <a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">More...</a><br /></td></tr>
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<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a9ab5fbbe154dd5b43fe272126d69411f">&#9670;&nbsp;</a></span>LDLT() <span class="overload">[1/4]</span></h2>

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<p>Default Constructor. </p>
<p>The default constructor is useful in cases in which the user intends to perform decompositions via LDLT::compute(const MatrixType&amp;). </p>

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<p>Default Constructor with memory preallocation. </p>
<p>Like the default constructor but with preallocation of the internal data according to the specified problem <em>size</em>. </p><dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1LDLT.html#a9ab5fbbe154dd5b43fe272126d69411f" title="Default Constructor.">LDLT()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ab45453a84ebb985cb0d1d9128b7af18d">&#9670;&nbsp;</a></span>LDLT() <span class="overload">[3/4]</span></h2>

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<p>Constructor with decomposition. </p>
<p>This calculates the decomposition for the input <em>matrix</em>.</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1LDLT.html#abd3c8856337dfc7f4df6214b9503dcf2" title="Default Constructor with memory preallocation.">LDLT(Index size)</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ad2f39b7a2a17c6e982db2e4164b6dd9f">&#9670;&nbsp;</a></span>LDLT() <span class="overload">[4/4]</span></h2>

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template&lt;typename MatrixType_ , int UpLo_&gt; </div>
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<p>Constructs a <a class="el" href="classEigen_1_1LDLT.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> factorization from a given matrix. </p>
<p>This overloaded constructor is provided for <a class="el" href="group__InplaceDecomposition.html">inplace decomposition </a> when <code>MatrixType</code> is a <a class="el" href="classEigen_1_1Ref.html" title="A matrix or vector expression mapping an existing expression.">Eigen::Ref</a>.</p>
<dl class="section see"><dt>See also</dt><dd>LDLT(const EigenBase&amp;) </dd></dl>

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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#af4fd7733fd47bc76d49d8dde08494195">&#9670;&nbsp;</a></span>adjoint()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the adjoint of <code>*this</code>, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.</dd></dl>
<p>This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as: </p><div class="fragment"><div class="line">x = decomposition.adjoint().solve(b) </div>
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<h2 class="memtitle"><span class="permalink"><a href="#a18589fe69cc1286c3da6ad894813899c">&#9670;&nbsp;</a></span>compute()</h2>

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template&lt;typename MatrixType_ , int UpLo_&gt; </div>
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<p>Compute / recompute the <a class="el" href="classEigen_1_1LDLT.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> decomposition A = L D L^* = U^* D U of <em>matrix</em> </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ae24d5a022e1c09d5afa0e84c356b854e">&#9670;&nbsp;</a></span>info()</h2>

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<p>Reports whether previous computation was successful. </p>
<dl class="section return"><dt>Returns</dt><dd><code>Success</code> if computation was successful, <code>NumericalIssue</code> if the factorization failed because of a zero pivot. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a87fc4b3b96a1f432374541defad416f9">&#9670;&nbsp;</a></span>isNegative()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if the matrix is negative (semidefinite) </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#aa1294edd3e62b4b1906918abc75ae50e">&#9670;&nbsp;</a></span>isPositive()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if the matrix is positive (semidefinite) </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a1c29cf5110c180a8fc5da40096822ed1">&#9670;&nbsp;</a></span>matrixL()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a view of the lower triangular matrix L </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a3b8250ff102497021676df9f8cb76113">&#9670;&nbsp;</a></span>matrixLDLT()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the internal <a class="el" href="classEigen_1_1LDLT.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> decomposition matrix</dd></dl>
<p>TODO: document the storage layout </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ae8be83b613c7fad1ad5d0a2b44c483e0">&#9670;&nbsp;</a></span>matrixU()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a view of the upper triangular matrix U </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a21a4d19e6c079967ee96c808a8e91d68">&#9670;&nbsp;</a></span>rankUpdate()</h2>

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template&lt;typename MatrixType_ , int UpLo_&gt; </div>
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<p>Update the <a class="el" href="classEigen_1_1LDLT.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T. </p><dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramname">w</td><td>a vector to be incorporated into the decomposition. </td></tr>
    <tr><td class="paramname">sigma</td><td>a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column vectors. Optional; default value is +1. </td></tr>
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<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1LDLT.html#a3ed6b348086c7b4c117dbff35be1a16d">setZero()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a69bc9dfd866eab90646ca7b74e52c8bc">&#9670;&nbsp;</a></span>rcond()</h2>

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<dl class="section return"><dt>Returns</dt><dd>an estimate of the reciprocal condition number of the matrix of which <code>*this</code> is the <a class="el" href="classEigen_1_1LDLT.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> decomposition. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#adf2c9a2939f6c5f4e36a94d99d4aa49f">&#9670;&nbsp;</a></span>reconstructedMatrix()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the matrix represented by the decomposition, i.e., it returns the product: P^T L D L^* P. This function is provided for debug purpose. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a3ed6b348086c7b4c117dbff35be1a16d">&#9670;&nbsp;</a></span>setZero()</h2>

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<p>Clear any existing decomposition </p><dl class="section see"><dt>See also</dt><dd>rankUpdate(w,sigma) </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a20cfad0f8808c84d150d1f90abe1fc87">&#9670;&nbsp;</a></span>solve()</h2>

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          <td>(</td>
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<dl class="section return"><dt>Returns</dt><dd>a solution x of \( A x = b \) using the current decomposition of A.</dd></dl>
<p>This function also supports in-place solves using the syntax <code>x = decompositionObject.solve(x)</code> .</p>
<p>This method just tries to find as good a solution as possible. If you want to check whether a solution exists or if it is accurate, just call this function to get a result and then compute the error of this result, or use <a class="el" href="classEigen_1_1DenseBase.html#ae8443357b808cd393be1b51974213f9c">MatrixBase::isApprox()</a> directly, for instance like this:</p><div class="fragment"><div class="line"><span class="keywordtype">bool</span> a_solution_exists = (A*result).isApprox(b, precision); </div>
</div><!-- fragment --><p> This method avoids dividing by zero, so that the non-existence of a solution doesn't by itself mean that you'll get <code>inf</code> or <code>nan</code> values.</p>
<p>More precisely, this method solves \( A x = b \) using the decomposition \( A = P^T L D L^* P \) by solving the systems \( P^T y_1 = b \), \( L y_2 = y_1 \), \( D y_3 = y_2 \), \( L^* y_4 = y_3 \) and \( P x = y_4 \) in succession. If the matrix \( A \) is singular, then \( D \) will also be singular (all the other matrices are invertible). In that case, the least-square solution of \( D y_3 = y_2 \) is computed. This does not mean that this function computes the least-square solution of \( A x = b \) if \( A \) is singular.</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a0ecf058a0727a4cab8b42d79e95072e1">MatrixBase::ldlt()</a>, <a class="el" href="classEigen_1_1SelfAdjointView.html#a644155eef17b37c95d85b9f65bb49ac4">SelfAdjointView::ldlt()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a0779d1ee8b62a8a97275dc36db340a35">&#9670;&nbsp;</a></span>transpositionsP()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the permutation matrix P as a transposition sequence. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a1d536082297052c96f074c5e208bb7a8">&#9670;&nbsp;</a></span>vectorD()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the coefficients of the diagonal matrix D </dd></dl>

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<hr/>The documentation for this class was generated from the following file:<ul>
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